Whether we think a thermos is better at keeping things hot or cold is probably to some degree influenced by our perception of temperature differences. In general we may be more aware of changes in the temperature of hot liquids than cold liquids.
That said, the rate of heat transfer by conduction and convection is proportional to temperature difference, all else being equal. Therefore the greater the temperature difference between the contents of the thermos and room ambient, and contact surfaces at room temperature, the greater the heat transfer rate (the quicker the contents will warm or cool), all else being equal.
So given a difference in temperature between hot coffee, at say 80 C. and room temperature, at say 20 C, of 60C, compared to the difference between water at 0 C and room temperature of 20 C, the initial rate of cooling of the coffee would be three times greater than the rate of warming of the cold water. If you had a mixture of ice and water it would warm even more slowly because of the latent heat of fusion of the ice.
However, as time goes on and the temperature difference between the contents and the room narrow, so will the differences in heat transfer rates narrow.
Hope this helps.